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# Integra

## Description

A single processor public domain Fortran-77 program by Alfio Borzí to solve nonlinear integral equations using a multigrid method.

The INTEGRA code was originally implemented to solve the thermodynamic Bethe ansatz problem which provides a means to link a conjectured scattering theory with the underlying field theory. This application of the code is described in Alfio Borzí and Anni Koubek, Computer Physics Communications 75 (1993) 118-126.

However, INTEGRA is a general code for integral equations. It does not contain the most sophisticated MG techniques for this type of problems, but it can be useful to those who would like to use or learn multigrid to solve integral equations.

The INTEGRA code is an implementation of the nonlinear multigrid method for the solution of systems of nonlinear Fredholm integral equations of the second kind:

/ bb
ui(y)=tni(y)+| sum_j( | fij(y,x,u(x))dx) , i=0,..,nsys, j=0,..,nsys,
/-bb

where nsys is the number of equations, fij are the kernels, x one-dimensional. The bounds -b and b are determined by the code corresponding to the region where the kernel functions are zero to some tolerance. The initial approximation is taken to be ui=tni=ri*gni, where the ri's are given in the input file coeff.dat. The other input file, integra.dat, contains multigrid related data.

The convergence properties of INTEGRA are analyzed in . The data structure of this code is as given in . This code is an implementation of the Nonlinear Multi-Grid Method of the Second Kind (FAS scheme), which is described in .

This is a public domain code. The program is provided AS IS without warranty of any kind.

References
1. Alfio Borzí and Anni Koubek, On a Multi-Grid Algorithm for the TBA Equations, in P.W. Hemker and P. Wesseling (Eds.), Multigrid Methods IV, International Series on Numerical Mathematics, Vol. 116, Birkhäuser Verlag, Basel, 1994.
2. A. Brandt, Multi-Level Adaptive Solutions to Boundary-Value Problems, Mathematics of Computation 31 (1977), pp. 333-390.
3. W. Hackbusch, Multi-Grid Methods and Applications, Springer-Verlag, Berlin, 1985.
Archive Contents

The archive integra.tgz or integra.zip has 21 files:

```integra:
total 176
-rw-r--r--   484 Jan 24  2000 bound.f
-rw-r--r--    41 Sep  4  2006 coeff.dat
-rw-r--r--   424 Jan 24  2000 crsres.f
-rw-r--r--   332 Jan 24  2000 f.f
-rw-r--r--   264 Jan 24  2000 grdfn.f
-rw-r--r--  1010 Jan 24  2000 intadd.f
-rw-r--r--    83 Sep  4  2006 integra.dat
-rw-r--r--  5931 Jan 24  2000 integra.f
-rw-r--r--   931 Jan 24  2000 intrp3.f
-rw-r--r--   573 Jan 24  2000 kappau.f
-rw-r--r--   340 Jan 24  2000 key.f
-rw-r--r--   201 Jan 24  2000 mytime.f
-rw-r--r--  1430 Jan 24  2000 nlni.f
-rw-r--r--  1426 Jan 24  2000 nmgm.f
-rw-r--r--   676 Jan 24  2000 printsol.f
-rw-r--r--   316 Jan 24  2000 putf.f
-rw-r--r--   398 Jan 24  2000 putu.f
-rw-r--r--   728 Jan 24  2000 relax.f
-rw-r--r--   531 Jan 24  2000 rescal.f
-rw-r--r--   238 Jan 24  2000 tn.f
-rw-r--r--   258 Jan 24  2000 u.f
```

Cheers,
Craig C. Douglas

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